Conway's big picture, see [1]} or section 2, is the Hasse diagram of a wonderful poset structure on the cosets \(PSL_2(\mathbb {Z}) \backslash PGL_2^+(\mathbb {Q})\) , classifying projective classes of commensurable integral lattices of rank two. It was introduced to understand discrete groups like the congruence subgroups \(\Gamma _0(N)\)  and their normalizers in \(PSL_2(\mathbb {R})\) , in particular the genus zero groups appearing in monstrous moonshine [2]}. Later, it turned out to be important in Connes' approach to the Riemann hypothesis, see [3]} or [4]}, as its vertices form a basis for the regular representation of the Bost-Connes algebra, see also [5]} or [6]}. This algebra encodes the action of the absolute Galois group on the roots of unity.
